Knaub, Karl R2009-10-062009-10-062001b4688245549527083Thesis 50761http://hdl.handle.net/1773/6772Thesis (Ph. D.)--University of Washington, 2001We study the behavior of solutions of certain parabolic partial differential equations of the form ut = epsilon2 uxx + epsilong(u) ux + h(u) in the limit epsilon → 0+. Solutions of advection-diffusion and reaction-diffusion equations are specifically considered. These solutions possess slowly moving internal layers, the positions of which are often of physical interest. Previous studies have focused on solutions which exhibit exponential asymptotics; we broaden the class studied to include the more common algebraic asymptotics. Metastability and supersensitivity are also considered in both cases.vi, 100 p.en-USCopyright is held by the individual authors.Theses--Applied mathematicsThesis